Question

D
С
11. In a AABC, D is the mid-point of side BC
and E is the mid-point of AD. BE produced
meets AC at F. Prove that F is the point
of trisection of line AC.​

Answer 1

Answer:

Step-by-step explanation:

PROVE : AF : FC = ?

CONSTRUCTION: DG // BF

PROOF : In triangle ADG,

AE = ED ( given)

EF // DG ( by construction)

So AF = FG……. ………(1) (a line passing through the mid point of any side of a triangle, parallel to the other side, bisects the third side)

Now in triangle CBF

BD = DC ( given)

DG // BF ( by construction)

So, FG = GC ( Same reason) ……..(2)

Now, by (1) & (2)

AF = FG = GC

=> AF : FC = 1:2

[Hence Proved]